# Logic Design for Array-Based Circuits

### by Donnamaie E. White

Copyright © 1996, 2001, 2002 Donnamaie E. White

# Faults and Fault Detection

Last Edit July 22, 2001

### Formation Rules for the Existence Function

The inputs and outputs for a vector represent a point on the Existence function map that has a value of one. The set of all points of value equal to one is the Existence Function.

A Test Sequence is a sequence of tests or input vectors represented by a selected sequencing through the points of the Existence Function. A Minimal Test Sequence may not necessarily use all Existence Function points (minterms, vectors). The existence function for the sample circuit of Figure 9-2 is shown in Figure 9-3.

Figure 9.3 Sample Circuit (2-Stage NAND)

The points on the Existence Function, treated as minterms, are linked following the linkage rule:

Two points connect if and only if:

• The input variables are logical distance one
• A primary output variable toggles 0-1 or 1-0

Logical distance one for the input variables means that only one input variable may change state when traversing the link from one minterm to another. The primary output must be an observable output (as shown in Figure 9-4.)

The requirement that only one input change per vector is designed to reduce the instance of hazards and race conditions in the test vector set. Hazards are introduced during test when multiple inputs change state due to differences in the tester lead connections. The parametric vectors for the gate tree in the last chapter are written using the Minimal Test Sequence for the tree.

Figure 9-4 Adding The Logical-Distance-One Edges

### Selecting a Chain

When all the possible links have been formed, there will be one or more observable chains or sets of links. The longest chain defines the desired Test Sequence.

Copyright @ 2001, 2002 Donnamaie E. White, White Enterprises
For problems or questions on these pages, contact dew@Donnamaie.com